Thermodynamics of the brane

TL;DR

This paper investigates the thermodynamic properties and meson spectra of D-brane probe systems in black hole backgrounds, revealing phase transitions and instabilities in finite-temperature gauge theories with flavors.

Contribution

It extends previous work by calculating free energy, entropy, energy densities, and meson spectra, highlighting phase transitions and tachyonic instabilities.

Findings

First order phase transition with meson melting

Tachyonic modes indicate instability in certain embeddings

Thermodynamic quantities computed match phase transition expectations

Abstract

The holographic dual of a finite-temperature gauge theory with a small number of flavours typically contains D-brane probes in a black hole background. We have recently shown that these systems undergo a first order phase transition characterised by a `melting' of the mesons. Here we extend our analysis of the thermodynamics of these systems by computing their free energy, entropy and energy densities, as well as the speed of sound. We also compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from thermodynamic considerations.